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Table T(n,k) read by upward antidiagonals. T(n,k) = Product_{i=1..n} Sum_{j=1..k} (i-1)*k+j
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%I #13 Mar 31 2020 10:40:32

%S 1,2,3,6,21,6,24,231,90,10,120,3465,2160,260,15,720,65835,71280,10920,

%T 600,21,5040,1514205,2993760,633360,39000,1197,28,40320,40883535,

%U 152681760,46868640,3510000,111321,2156,36,362880,1267389585,9160905600,4218177600

%N Table T(n,k) read by upward antidiagonals. T(n,k) = Product_{i=1..n} Sum_{j=1..k} (i-1)*k+j

%C T(n,k) is the minimum value of Product_{i=1..n} Sum_{j=1..k} r[(i-1)*k+j] among all permutations r of {1..kn}. For the maximum value see A333420.

%H Chai Wah Wu, <a href="https://arxiv.org/abs/2002.10514">On rearrangement inequalities for multiple sequences</a>, arXiv:2002.10514 [math.CO], 2020.

%F T(n,k) = k^(2n)*Gamma(n+(1+k)/2k)/Gamma((1+k)/2k).

%o (Python)

%o def T(n,k): # T(n,k) for A333445

%o c, l = 1, list(range(1,k*n+1,k))

%o lt = list(l)

%o for i in range(n):

%o for j in range(1,k):

%o lt[i] += l[i]+j

%o c *= lt[i]

%o return c

%K nonn,tabl

%O 1,2

%A _Chai Wah Wu_, Mar 23 2020